That sounds like a "dry joint" somewhere, or a control that's not making good contact. (Assuming you are not using any pedals - disconnect them while you test, if you are). Unplug and reconnect each cable a few times to clean the contacts.
Also plug and unplug something in to any "Effect loop" or other auxiliary sockets on the amp - some have switch contact in the sockets which can tarnish and act up over time. Move all the controls / switches on the amp and guitar over their full range / every position a few times. (Nothing has to be switched on while doing all that).
If it still does not work try unplugging the lead at the guitar end and very lightly touch the tip while holding the cable by the insulation - you should get a buzz through the amp. If not, it's most likely a fault in the amp. Otherwise, it's probably a bad joint in the guitar.
(Or try a different guitar & see if the fault is still present). You can clean the plugs using a cloth with a trace of light oil such as Dunlop Lemon oil, 3-in-one or WD40 to help prevent tarnish. Don't use enough to leave them greasy, just a fine trace to protect the surfaces from air.
Work them in each socket a few times to transfer some to the contact surfaces in those as well.
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